An image or video camera captures a significant amount of data when acquiring image or video data. In order to store or transmit the acquired data, this data is typically compressed after the video is captured. This compression typically exploits a priori knowledge such as the fact that an N-pixel image can be approximated as a sparse linear combination of wave-length coefficients K, which are less than the N pixels. The wavelength coefficients can be computed from the N pixel values, and then stored or transmitted along with their locations. The standard procedure for transform coding of sparse signals is to acquire the full N-sample signal, compute the complete set of transform coefficients, locate the K largest, significant coefficients and discard the many small coefficients, and encode the values and locations of the largest coefficients. When N is large and K is small, this process is inefficient. However, acquiring large amounts of raw image or video data (large N) can be expensive, particularly at wave-lengths where CMOS or CCD sensing technology is limited. Also, compressing raw data can be computationally demanding.
One conventional approach uses compressive imaging to directly acquire random projections without first collecting the N pixels. For instance, the conventional approach applies a measurement basis to the data captured by the optical lens (e.g., before the pixel values are obtained) to obtain a series of measurements, which represent the encoded data. As such, the conventional method directly acquires the reduced set of measurements of an N-pixel image without first acquiring the N pixel values. However, this conventional approach has disadvantages when capturing video data. For example, the conventional approach performs only spatial projection/integration using snapshots of an image without temporal integration. Video data is localized into a different two-dimensional (2D) snapshot for each measurement. As such, this method loses information between snapshots, or must acquire a large amount of data to capture fast actions.